Fuel pressure unstable

The fuel pressure regulator is adjusted by intake manifold vacuum. You have fuel pressure pushing fuel through the injector, and manifold vacuum pulling it. During coasting, vacuum goes up, and that would cause an excessively-rich mixture. Instead, the regulator responds by reducing fuel pressure. That lower pressure offsets the higher vacuum, so the net force working on the fuel molecules remains constant.

The opposite happens when accelerating. Vacuum goes down, so the regulator increases fuel pressure to again, maintain a constant force on the fuel. If your engine runs near fifty pounds of fuel pressure, you will typically see that pressure go up and down roughly five pounds as vacuum changes.

That vibrating needle is normal. The fuel pressure regulator uses a spring-loaded metal valve to block fuel from flowing into the return line that goes back to the tank. The stronger the spring, the higher the fuel pressure. Manifold vacuum pulls against that spring to make the valve open easier. As vacuum goes up, it helps the valve open, so it does not keep the fuel under as much pressure. The pressure drops, and the volume of fuel going back into the tank increases. It is normal for that valve to vibrate a little, as you are seeing on the gauge.

For the larger oscillations about two times per second, pull the vacuum hose off the regulator and plug it. If those pulses stop, they are due to pulsing manifold vacuum. That can be from erratic idle speed or emissions systems pulsing on and off. One suspect is the charcoal canister purge solenoid. Those do not stay open when activated. They cycle on and off, about two times per second.

The changes you are seeing on the gauge should not cause an engine running problem.